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C3×C17⋊(D43⋊C3) #27190481

order13158
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17⋊(D43⋊C3)
unambiguous semidirect productC17⋊(C3×D43⋊C3)
unambiguous semidirect product(C43⋊C3)⋊(C3×D17)
unambiguous semidirect productD731⋊C32
unambiguous semidirect product(C3×D731)⋊C3

Splittings

Fitting, socleC3×C17×C43 ⋊ C2×C3
derived, HallC17×C43 ⋊ C2×C32
HallC3×C17×C43⋊C3 ⋊ C2
HallD731 ⋊ C32
HallC3×C43⋊C3 ⋊ D17
SylowC43 ⋊ C32×D17
SylowC17 ⋊ C3×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C17⋊(D43⋊C3)
commutator, cosocle, hypocenterC17×C43C2×C32
FrattiniC1G
Fitting, socleC3×C17×C43C2×C3
LCSG ▷ C17×C43
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 2193

A minimal faithful permutation representation — 2 generators on 63 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,36)(12,26,22,20,16,13)(19,32,34,23,25,37)(21,38,39,30,29,33)(31,41,42,40,35,43)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60);(1,2,5,11,19,22,7,6,12,21,31,39,15,26,14,25,35,42,28,37,38,27,18,29,34,36,43,41,32,10,16,24,33,40,30,20,4,8,13,23,17,9,3)(44,45,47,49,51,53,55,57,59,60,58,56,54,52,50,48,46)(61,62,63)

Conjugacy classes & character table

447 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D17×D43⋊C3, D3×C17⋊(D43⋊C3), D51⋊(D43⋊C3), …
maximal normal subgroup ofC3×D17×D43⋊C3, D3×C17⋊(D43⋊C3), D51⋊(D43⋊C3), …
maximal quotient ofC3×(C43⋊C3)⋊Dic17, C2×C3×C17⋊(D43⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 15);